In this paper, we give the definition of local variable Morrey–Lorentz spaces ${\mathcal{M}}_{p(\cdot ),q(\cdot ),\lambda }^{loc}({\mathbb{R}}^n)$ which are a new class of functions. Also, we prove the boundedness of the Hardy–Littlewood maximal operator M and Calderón–Zygmund operators T on these spaces. Finally, we apply these results to the Bochner–Riesz operator $B_r^{\delta }$, identity approximation $A_{\epsilon }$ and the Marcinkiewicz operator ${\mu }_{\mathrm{\Omega }}$ on the spaces ${\mathcal{M}}_{p(\cdot ),q(\cdot ),\lambda }^{loc}({\mathbb{R}}^n)$.

中文翻译：

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局部变量 Morrey-Lorentz 空间上的极大值和 Calderón-Zygmund 算子及一些应用

在本文中，我们给出局部变量 Morrey-Lorentz 空间的定义${\mathcal{米}}_{p(\cdot ),q(\cdot ),\lambda }^{升oC}({\mathbb{R}}^n)$这是一类新的功能。此外，我们证明了 Hardy–Littlewood 极大算子M和 Calderón–Zygmund 算子T在这些空间上的有界性。最后，我们将这些结果应用于 Bochner–Riesz 算子${乙}_r^{\delta }$, 恒等式近似$A_{\epsilon }$和 Marcinkiewicz 算子${\mu }_{\mathrm{欧姆}}$在空格上${\mathcal{米}}_{p(\cdot ),q(\cdot ),\lambda }^{升oC}({\mathbb{R}}^n)$.